Internal combustion engines having operating types also designated as HCCI (homogeneous charge compression ignition) are known, in which fuel is injected directly into a combustion chamber and ignites itself comparable to the Diesel principle. The HCCI combustion methods are used in internal combustion engines otherwise operated using externally supplied ignition, especially because of their high potential for reduction in fuel usage and reduction in emissions. Since the stability of HCCI combustion methods is generally very sensitive with respect to changed boundary conditions, such as environmental temperature, variances in a valve system of the internal combustion engine, environmental pressure, aging of components of the internal combustion engine and the like, usual HCCI combustion methods provide using a relatively large quantity of hot residual gas for a cylinder charge, this gas being introduced into the combustion chamber by way of internal or external exhaust-gas recirculation by an appropriate design and activation of gas exchange valves. In the known HCCI combustion methods, this achieves a sufficiently great cylinder temperature, which has a positive effect on the stability of the combustion process, and makes the combustion or ignition possible in the first place. Because of the relatively large proportion of residual gas of the cylinder charge in the usual HCCI combustion methods, the fresh air proportion in the corresponding cylinder is reduced, whereby the calorific properties of the air/fuel mixture, present in the combustion chamber of the cylinder, deteriorate, so that the fuel usage of the internal combustion engine is also increased.